Among the many candidates proposed to explain nature of Dark Matter, Weakly Interacting Massive Particles have been the most supported in the last decades, because of their natural explanation of the Dark Matter abundance and their connection to the hierarchy problem. Other intriguing candidates are Primordial Black Holes. In this Thesis we touch on both frameworks for the explanation of Dark Matter. As for WIMP candidates, we discuss two possible theoretical frameworks. On the side of Effective Field Theories, we propose a method to use them consistently for the recast of collider searches. As for simplified models, in presence of gauge anomalies we highlight the enhanced reach of indirect searches. Then we illustrate a model for the generation of Primordial Black Holes relying on the metastability of the Higgs vacuum. Another signature of this remarkable property of the Standard Model could be the generation of a background of gravitational waves.